Electrothermal Simulation and Optimal Design of Thermoelectric Cooler Using Analytical Approach
Electrothermal Simulation and Optimal Design of Thermoelectric Cooler Using Analytical Approach
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DOI：
10.1109/tcad.2021.3120533
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发表时间：
2021-10
影响因子：
2.9
通讯作者：
Liang Chen;Sheriff Sadiqbatcha;H. Amrouch;S. Tan
中科院分区：
文献类型：
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作者：
Liang Chen;Sheriff Sadiqbatcha;H. Amrouch;S. Tan
通过求解耦合的热传导和电流连续性方程，对VLSI系统封装设计中的热电制冷(TEC)进行了电热建模和仿真。我们给出了描述温度和电压的耦合偏微分方程组(PDE)的一个新的解析解。此外，我们还推导了TEC器件的两个关键性能指标的新的解析表达式：1)最大温差和2)最大热流泵送能力，这可以指导热电制冷器的优化设计，以实现最大的制冷性能。此外，我们还首次观察到当无因次优值系数$ZT_{0}>1时，没有最大热流量值，这意味着Peltier和傅立叶传递效应引起的散热大于焦耳加热效应产生的热量，这将导致更有效的TEC冷却设计。用COMSOL软件进行三维有限元计算，验证了所提出的一维有限元公式的准确性。与COMSOL相比，紧凑型模型提供了数个数量级的加速比和内存节省，但精度损失不大。与传统的简化一维能量平衡模型相比，所提出的解析耦合多物理模型具有更强的稳健性和更高的精度。
In this article, electrothermal modeling and simulation of thermoelectric cooling (TEC) in the package design of VLSI systems are performed by solving coupled heat conduction and current continuity equations. We propose a new analytical solution to the coupled partial differential equations (PDEs) which describe temperature and voltage with the reduction from 3-D to 1-D. In addition to this, we derive new analytic expressions for two key performance metrics for TEC devices: 1) the maximum temperature difference and 2) the maximum heat-flux pumping capability, which can be guided for the optimal design of thermoelectric cooler to achieve the maximum cooling performance. Furthermore, for the first time, we observe that when the dimensionless figure of merit $ZT_{0}$ value is larger than 1, there is no maximum heat-flux value, which means the heat dissipation due to the Peltier and Fourier transfer effects is larger than the heat generation caused by the Joule heating effect, which can lead to more efficient TEC cooling design. The accuracy of the proposed 1-D formulas is verified by a 3-D finite element method using COMSOL software. The compact model delivers many orders of magnitude speedup and memory saving compared to COMSOL with marginal accuracy loss. Compared with the conventional simplified 1-D energy equilibrium model, the proposed analytical coupled multiphysics model is more robust and accurate.